Trying to upgrade hotel room

Alright, I'll keep it simple.

My older brother and I booked a small two-bed room at a 4-Star in Budapest for seven nights, starting five hours ago.

He's taking me around Europe (or rather, paying for me to take him around Europe, as I've been around here the last year) as a graduation present.

He's an engineer. If you were raised by engineers / have engineer siblings, you know they are a different breed, and hence this is relevant.

We just checked in, he's off wandering around and I'm about to go eat, so the request won't happen at least for an hour and a half ...?

But the hotel room has a broken shower head (it won't stay pointed up, it won't stay vertically up on the adjusting post), and the shower door leaks. I also stepped on a blueberry that looked like it had been there a while. Otherwise it's more or less fine.

Instead of just a room change (no way in hell I'm staying in a room for a week with a broken shower head), how can my brother and I turn this into a room upgrade? I've heard, well, be nice about it, be respectful, perhaps seem exhausted but still in a good mood, and more than less, just ask.

Do any of you have experience with this? I kinda worry that my engineer brother would just get us another room of the same type rather than an upgrade, so I'm hoping for advice and stories to help me get a better idea of how to go about this. If it's impossible, I'll let it be, but I am of the mindset that nothing, if approached correctly, is impossible.

Thank you much,
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IDS